where \(\Gamma (x)\)  is the gamma function.
For bilayer graphene, \(N = 2\) , then \(g_2 (\infty ) = 1.854\)  and \(\Delta (T=0) = 1.719 \alpha _{\mathrm {g}}^2 \gamma _1\) , whereas, for \(N \gg 1\) , then \(g_N (\infty ) = 1\)  and \(\Delta (T=0) = \alpha _{\mathrm {g}} \gamma _1\) .
For finite \(T\) , the temperature dependence of the order parameter (REF ) is similar to the self-consistent equation for the magnetization in the Weiss mean-field approximation [1]} and, for \(N \gg 1\) , we find that the critical temperature is given by \(k_{\mathrm {B}}T_{\mathrm {c}} = \alpha _{\mathrm {g}} \gamma _1/4\) .
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